| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Data.Monoid.Compat
Synopsis
- newtype Any = Any {}
- newtype Sum a = Sum {
- getSum :: a
- newtype Product a = Product {
- getProduct :: a
- newtype Last a = Last {}
- newtype First a = First {}
- class Semigroup a => Monoid a where
- newtype Alt (f :: k -> Type) (a :: k) = Alt {
- getAlt :: f a
- newtype All = All {}
- newtype Endo a = Endo {
- appEndo :: a -> a
- newtype Dual a = Dual {
- getDual :: a
- newtype Ap (f :: k -> Type) (a :: k) = Ap {
- getAp :: f a
- (<>) :: Semigroup a => a -> a -> a
Documentation
Boolean monoid under disjunction (||).
Any x <> Any y = Any (x || y)
Examples
>>>Any True <> mempty <> Any FalseAny {getAny = True}
>>>mconcat (map (\x -> Any (even x)) [2,4,6,7,8])Any {getAny = True}
>>>Any False <> memptyAny {getAny = False}
Instances
| Data Any | Since: base-4.8.0.0 | ||||
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any # dataTypeOf :: Any -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Any) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) # gmapT :: (forall b. Data b => b -> b) -> Any -> Any # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r # gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any # | |||||
| Monoid Any | Since: base-2.1 | ||||
| Semigroup Any | Since: base-4.9.0.0 | ||||
| Bounded Any | Since: base-2.1 | ||||
| Generic Any | |||||
Defined in Data.Semigroup.Internal Associated Types
| |||||
| Read Any | Since: base-2.1 | ||||
| Show Any | Since: base-2.1 | ||||
| Eq Any | Since: base-2.1 | ||||
| Ord Any | Since: base-2.1 | ||||
| type Rep Any | Since: base-4.7.0.0 | ||||
Defined in Data.Semigroup.Internal | |||||
Monoid under addition.
Sum a <> Sum b = Sum (a + b)
Examples
>>>Sum 1 <> Sum 2 <> memptySum {getSum = 3}
>>>mconcat [ Sum n | n <- [3 .. 9]]Sum {getSum = 42}
Instances
| MonadFix Sum | Since: base-4.8.0.0 | ||||
Defined in Control.Monad.Fix | |||||
| MonadZip Sum | Since: base-4.8.0.0 | ||||
| Foldable Sum | Since: base-4.8.0.0 | ||||
Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldMap' :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # | |||||
| Foldable1 Sum | Since: base-4.18.0.0 | ||||
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Sum m -> m # foldMap1 :: Semigroup m => (a -> m) -> Sum a -> m # foldMap1' :: Semigroup m => (a -> m) -> Sum a -> m # toNonEmpty :: Sum a -> NonEmpty a # maximum :: Ord a => Sum a -> a # minimum :: Ord a => Sum a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Sum a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Sum a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Sum a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Sum a -> b # | |||||
| Traversable Sum | Since: base-4.8.0.0 | ||||
| Applicative Sum | Since: base-4.8.0.0 | ||||
| Functor Sum | Since: base-4.8.0.0 | ||||
| Monad Sum | Since: base-4.8.0.0 | ||||
| Generic1 Sum | |||||
Defined in Data.Semigroup.Internal Associated Types
| |||||
| Data a => Data (Sum a) | Since: base-4.8.0.0 | ||||
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sum a -> c (Sum a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) # dataTypeOf :: Sum a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) # gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r # gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) # | |||||
| Num a => Monoid (Sum a) | Since: base-2.1 | ||||
| Num a => Semigroup (Sum a) | Since: base-4.9.0.0 | ||||
| Bounded a => Bounded (Sum a) | Since: base-2.1 | ||||
| Generic (Sum a) | |||||
Defined in Data.Semigroup.Internal Associated Types
| |||||
| Num a => Num (Sum a) | Since: base-4.7.0.0 | ||||
| Read a => Read (Sum a) | Since: base-2.1 | ||||
| Show a => Show (Sum a) | Since: base-2.1 | ||||
| Eq a => Eq (Sum a) | Since: base-2.1 | ||||
| Ord a => Ord (Sum a) | Since: base-2.1 | ||||
| type Rep1 Sum | Since: base-4.7.0.0 | ||||
Defined in Data.Semigroup.Internal | |||||
| type Rep (Sum a) | Since: base-4.7.0.0 | ||||
Defined in Data.Semigroup.Internal | |||||
Monoid under multiplication.
Product x <> Product y == Product (x * y)
Examples
>>>Product 3 <> Product 4 <> memptyProduct {getProduct = 12}
>>>mconcat [ Product n | n <- [2 .. 10]]Product {getProduct = 3628800}
Constructors
| Product | |
Fields
| |
Instances
| MonadFix Product | Since: base-4.8.0.0 | ||||
Defined in Control.Monad.Fix | |||||
| MonadZip Product | Since: base-4.8.0.0 | ||||
| Foldable Product | Since: base-4.8.0.0 | ||||
Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldMap' :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # | |||||
| Foldable1 Product | Since: base-4.18.0.0 | ||||
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Product m -> m # foldMap1 :: Semigroup m => (a -> m) -> Product a -> m # foldMap1' :: Semigroup m => (a -> m) -> Product a -> m # toNonEmpty :: Product a -> NonEmpty a # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Product a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Product a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Product a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Product a -> b # | |||||
| Traversable Product | Since: base-4.8.0.0 | ||||
| Applicative Product | Since: base-4.8.0.0 | ||||
| Functor Product | Since: base-4.8.0.0 | ||||
| Monad Product | Since: base-4.8.0.0 | ||||
| Generic1 Product | |||||
Defined in Data.Semigroup.Internal Associated Types
| |||||
| Data a => Data (Product a) | Since: base-4.8.0.0 | ||||
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Product a -> c (Product a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) # toConstr :: Product a -> Constr # dataTypeOf :: Product a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) # gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r # gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # | |||||
| Num a => Monoid (Product a) | Since: base-2.1 | ||||
| Num a => Semigroup (Product a) | Since: base-4.9.0.0 | ||||
| Bounded a => Bounded (Product a) | Since: base-2.1 | ||||
| Generic (Product a) | |||||
Defined in Data.Semigroup.Internal Associated Types
| |||||
| Num a => Num (Product a) | Since: base-4.7.0.0 | ||||
Defined in Data.Semigroup.Internal | |||||
| Read a => Read (Product a) | Since: base-2.1 | ||||
| Show a => Show (Product a) | Since: base-2.1 | ||||
| Eq a => Eq (Product a) | Since: base-2.1 | ||||
| Ord a => Ord (Product a) | Since: base-2.1 | ||||
| type Rep1 Product | Since: base-4.7.0.0 | ||||
Defined in Data.Semigroup.Internal | |||||
| type Rep (Product a) | Since: base-4.7.0.0 | ||||
Defined in Data.Semigroup.Internal | |||||
Maybe monoid returning the rightmost non-Nothing value.
is isomorphic to Last a, and thus to
Dual (First a)Dual (Alt Maybe a)
Data.Semigroup.Last. The former returns the last non-Nothing,
so x <> Data.Monoid.Last Nothing = x. The latter simply returns the last value,
thus x <> Data.Semigroup.Last Nothing = Data.Semigroup.Last Nothing.
Examples
>>>Last (Just "hello") <> Last Nothing <> Last (Just "world")Last {getLast = Just "world"}
>>>Last Nothing <> memptyLast {getLast = Nothing}
Instances
| MonadFix Last | Since: base-4.8.0.0 | ||||
Defined in Control.Monad.Fix | |||||
| MonadZip Last | Since: base-4.8.0.0 | ||||
| Foldable Last | Since: base-4.8.0.0 | ||||
Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |||||
| Traversable Last | Since: base-4.8.0.0 | ||||
| Applicative Last | Since: base-4.8.0.0 | ||||
| Functor Last | Since: base-4.8.0.0 | ||||
| Monad Last | Since: base-4.8.0.0 | ||||
| Generic1 Last | |||||
Defined in Data.Monoid Associated Types
| |||||
| Data a => Data (Last a) | Since: base-4.8.0.0 | ||||
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) # toConstr :: Last a -> Constr # dataTypeOf :: Last a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) # gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r # gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # | |||||
| Monoid (Last a) | Since: base-2.1 | ||||
| Semigroup (Last a) | Since: base-4.9.0.0 | ||||
| Generic (Last a) | |||||
Defined in Data.Monoid Associated Types
| |||||
| Read a => Read (Last a) | Since: base-2.1 | ||||
| Show a => Show (Last a) | Since: base-2.1 | ||||
| Eq a => Eq (Last a) | Since: base-2.1 | ||||
| Ord a => Ord (Last a) | Since: base-2.1 | ||||
| type Rep1 Last | Since: base-4.7.0.0 | ||||
Defined in Data.Monoid | |||||
| type Rep (Last a) | Since: base-4.7.0.0 | ||||
Defined in Data.Monoid | |||||
Maybe monoid returning the leftmost non-Nothing value.
is isomorphic to First a, but precedes it
historically.Alt Maybe a
Beware that Data.Monoid.First is different from
Data.Semigroup.First. The former returns the first non-Nothing,
so Data.Monoid.First Nothing <> x = x. The latter simply returns the first value,
thus Data.Semigroup.First Nothing <> x = Data.Semigroup.First Nothing.
Examples
>>>First (Just "hello") <> First Nothing <> First (Just "world")First {getFirst = Just "hello"}
>>>First Nothing <> memptyFirst {getFirst = Nothing}
Instances
| MonadFix First | Since: base-4.8.0.0 | ||||
Defined in Control.Monad.Fix | |||||
| MonadZip First | Since: base-4.8.0.0 | ||||
| Foldable First | Since: base-4.8.0.0 | ||||
Defined in Data.Foldable Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |||||
| Traversable First | Since: base-4.8.0.0 | ||||
| Applicative First | Since: base-4.8.0.0 | ||||
| Functor First | Since: base-4.8.0.0 | ||||
| Monad First | Since: base-4.8.0.0 | ||||
| Generic1 First | |||||
Defined in Data.Monoid Associated Types
| |||||
| Data a => Data (First a) | Since: base-4.8.0.0 | ||||
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) # toConstr :: First a -> Constr # dataTypeOf :: First a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) # gmapT :: (forall b. Data b => b -> b) -> First a -> First a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r # gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) # | |||||
| Monoid (First a) | Since: base-2.1 | ||||
| Semigroup (First a) | Since: base-4.9.0.0 | ||||
| Generic (First a) | |||||
Defined in Data.Monoid Associated Types
| |||||
| Read a => Read (First a) | Since: base-2.1 | ||||
| Show a => Show (First a) | Since: base-2.1 | ||||
| Eq a => Eq (First a) | Since: base-2.1 | ||||
| Ord a => Ord (First a) | Since: base-2.1 | ||||
| type Rep1 First | Since: base-4.7.0.0 | ||||
Defined in Data.Monoid | |||||
| type Rep (First a) | Since: base-4.7.0.0 | ||||
Defined in Data.Monoid | |||||
class Semigroup a => Monoid a where #
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:
- Right identity
x<>mempty= x- Left identity
mempty<>x = x- Associativity
x(<>(y<>z) = (x<>y)<>zSemigrouplaw)- Concatenation
mconcat=foldr(<>)mempty
You can alternatively define mconcat instead of mempty, in which case the
laws are:
- Unit
mconcat(purex) = x- Multiplication
mconcat(joinxss) =mconcat(fmapmconcatxss)- Subclass
mconcat(toListxs) =sconcatxs
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define newtypes and make those instances
of Monoid, e.g. Sum and Product.
NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.
Methods
Identity of mappend
Examples
>>>"Hello world" <> mempty"Hello world"
>>>mempty <> [1, 2, 3][1,2,3]
An associative operation
NOTE: This method is redundant and has the default
implementation since base-4.11.0.0.
Should it be implemented manually, since mappend = (<>)mappend is a synonym for
(<>), it is expected that the two functions are defined the same
way. In a future GHC release mappend will be removed from Monoid.
Fold a list using the monoid.
For most types, the default definition for mconcat will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.
>>>mconcat ["Hello", " ", "Haskell", "!"]"Hello Haskell!"
Instances
| Monoid ByteArray | Since: base-4.17.0.0 |
| Monoid All | Since: base-2.1 |
| Monoid Any | Since: base-2.1 |
| Monoid Ordering | Since: base-2.1 |
| Monoid () | Since: base-2.1 |
| FiniteBits a => Monoid (And a) | This constraint is arguably too strong. However,
as some types (such as Since: base-4.16 |
| FiniteBits a => Monoid (Iff a) | This constraint is arguably
too strong. However, as some types (such as Since: base-4.16 |
| Bits a => Monoid (Ior a) | Since: base-4.16 |
| Bits a => Monoid (Xor a) | Since: base-4.16 |
| Monoid (Comparison a) |
mempty :: Comparison a mempty = Comparison _ _ -> EQ |
Defined in Data.Functor.Contravariant Methods mempty :: Comparison a # mappend :: Comparison a -> Comparison a -> Comparison a # mconcat :: [Comparison a] -> Comparison a # | |
| Monoid (Equivalence a) |
mempty :: Equivalence a mempty = Equivalence _ _ -> True |
Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a # mappend :: Equivalence a -> Equivalence a -> Equivalence a # mconcat :: [Equivalence a] -> Equivalence a # | |
| Monoid (Predicate a) |
mempty :: Predicate a mempty = _ -> True |
| Monoid a => Monoid (Identity a) | Since: base-4.9.0.0 |
| Monoid (First a) | Since: base-2.1 |
| Monoid (Last a) | Since: base-2.1 |
| Monoid a => Monoid (Down a) | Since: base-4.11.0.0 |
| (Ord a, Bounded a) => Monoid (Max a) | Since: base-4.9.0.0 |
| (Ord a, Bounded a) => Monoid (Min a) | Since: base-4.9.0.0 |
| Monoid m => Monoid (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m # | |
| Monoid a => Monoid (Dual a) | Since: base-2.1 |
| Monoid (Endo a) | Since: base-2.1 |
| Num a => Monoid (Product a) | Since: base-2.1 |
| Num a => Monoid (Sum a) | Since: base-2.1 |
| Monoid a => Monoid (STM a) | Since: base-4.17.0.0 |
| (Generic a, Monoid (Rep a ())) => Monoid (Generically a) | Since: base-4.17.0.0 |
Defined in GHC.Generics Methods mempty :: Generically a # mappend :: Generically a -> Generically a -> Generically a # mconcat :: [Generically a] -> Generically a # | |
| Monoid p => Monoid (Par1 p) | Since: base-4.12.0.0 |
| Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
| Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Monoid a => Monoid (Solo a) | Since: base-4.15 |
| Monoid [a] | Since: base-2.1 |
| Monoid a => Monoid (Op a b) |
mempty :: Op a b mempty = Op _ -> mempty |
| Monoid (Proxy s) | Since: base-4.7.0.0 |
| Monoid (U1 p) | Since: base-4.12.0.0 |
| Monoid a => Monoid (ST s a) | Since: base-4.11.0.0 |
| (Monoid a, Monoid b) => Monoid (a, b) | Since: base-2.1 |
| Monoid b => Monoid (a -> b) | Since: base-2.1 |
| Monoid a => Monoid (Const a b) | Since: base-4.9.0.0 |
| (Applicative f, Monoid a) => Monoid (Ap f a) | Since: base-4.12.0.0 |
| Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0 |
| Monoid (f p) => Monoid (Rec1 f p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | Since: base-2.1 |
| (Monoid (f a), Monoid (g a)) => Monoid (Product f g a) | Since: base-4.16.0.0 |
| (Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) | Since: base-4.12.0.0 |
| Monoid c => Monoid (K1 i c p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | Since: base-2.1 |
| Monoid (f (g a)) => Monoid (Compose f g a) | Since: base-4.16.0.0 |
| Monoid (f (g p)) => Monoid ((f :.: g) p) | Since: base-4.12.0.0 |
| Monoid (f p) => Monoid (M1 i c f p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | Since: base-2.1 |
newtype Alt (f :: k -> Type) (a :: k) #
Monoid under <|>.
Alt l <> Alt r == Alt (l <|> r)
Examples
>>>Alt (Just 12) <> Alt (Just 24)Alt {getAlt = Just 12}
>>>Alt Nothing <> Alt (Just 24)Alt {getAlt = Just 24}
Since: base-4.8.0.0
Instances
| Generic1 (Alt f :: k -> Type) | |||||
Defined in Data.Semigroup.Internal Associated Types
| |||||
| MonadFix f => MonadFix (Alt f) | Since: base-4.8.0.0 | ||||
Defined in Control.Monad.Fix | |||||
| MonadZip f => MonadZip (Alt f) | Since: base-4.8.0.0 | ||||
| Foldable f => Foldable (Alt f) | Since: base-4.12.0.0 | ||||
Defined in Data.Foldable Methods fold :: Monoid m => Alt f m -> m # foldMap :: Monoid m => (a -> m) -> Alt f a -> m # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m # foldr :: (a -> b -> b) -> b -> Alt f a -> b # foldr' :: (a -> b -> b) -> b -> Alt f a -> b # foldl :: (b -> a -> b) -> b -> Alt f a -> b # foldl' :: (b -> a -> b) -> b -> Alt f a -> b # foldr1 :: (a -> a -> a) -> Alt f a -> a # foldl1 :: (a -> a -> a) -> Alt f a -> a # elem :: Eq a => a -> Alt f a -> Bool # maximum :: Ord a => Alt f a -> a # minimum :: Ord a => Alt f a -> a # | |||||
| Foldable1 f => Foldable1 (Alt f) | Since: base-4.18.0.0 | ||||
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Alt f m -> m # foldMap1 :: Semigroup m => (a -> m) -> Alt f a -> m # foldMap1' :: Semigroup m => (a -> m) -> Alt f a -> m # toNonEmpty :: Alt f a -> NonEmpty a # maximum :: Ord a => Alt f a -> a # minimum :: Ord a => Alt f a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Alt f a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Alt f a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Alt f a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Alt f a -> b # | |||||
| Contravariant f => Contravariant (Alt f) | |||||
| Traversable f => Traversable (Alt f) | Since: base-4.12.0.0 | ||||
| Alternative f => Alternative (Alt f) | Since: base-4.8.0.0 | ||||
| Applicative f => Applicative (Alt f) | Since: base-4.8.0.0 | ||||
| Functor f => Functor (Alt f) | Since: base-4.8.0.0 | ||||
| Monad f => Monad (Alt f) | Since: base-4.8.0.0 | ||||
| MonadPlus f => MonadPlus (Alt f) | Since: base-4.8.0.0 | ||||
| (Data (f a), Data a, Typeable f) => Data (Alt f a) | Since: base-4.8.0.0 | ||||
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Alt f a -> c (Alt f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Alt f a) # toConstr :: Alt f a -> Constr # dataTypeOf :: Alt f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Alt f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Alt f a)) # gmapT :: (forall b. Data b => b -> b) -> Alt f a -> Alt f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r # gmapQ :: (forall d. Data d => d -> u) -> Alt f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Alt f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) # | |||||
| Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0 | ||||
| Alternative f => Semigroup (Alt f a) | Since: base-4.9.0.0 | ||||
| Enum (f a) => Enum (Alt f a) | Since: base-4.8.0.0 | ||||
| Generic (Alt f a) | |||||
Defined in Data.Semigroup.Internal Associated Types
| |||||
| Num (f a) => Num (Alt f a) | Since: base-4.8.0.0 | ||||
| Read (f a) => Read (Alt f a) | Since: base-4.8.0.0 | ||||
| Show (f a) => Show (Alt f a) | Since: base-4.8.0.0 | ||||
| Eq (f a) => Eq (Alt f a) | Since: base-4.8.0.0 | ||||
| Ord (f a) => Ord (Alt f a) | Since: base-4.8.0.0 | ||||
Defined in Data.Semigroup.Internal | |||||
| type Rep1 (Alt f :: k -> Type) | Since: base-4.8.0.0 | ||||
Defined in Data.Semigroup.Internal | |||||
| type Rep (Alt f a) | Since: base-4.8.0.0 | ||||
Defined in Data.Semigroup.Internal | |||||
Boolean monoid under conjunction (&&).
All x <> All y = All (x && y)
Examples
>>>All True <> mempty <> All False)All {getAll = False}
>>>mconcat (map (\x -> All (even x)) [2,4,6,7,8])All {getAll = False}
>>>All True <> memptyAll {getAll = True}
Instances
| Data All | Since: base-4.8.0.0 | ||||
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All # dataTypeOf :: All -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c All) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) # gmapT :: (forall b. Data b => b -> b) -> All -> All # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r # gmapQ :: (forall d. Data d => d -> u) -> All -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All # | |||||
| Monoid All | Since: base-2.1 | ||||
| Semigroup All | Since: base-4.9.0.0 | ||||
| Bounded All | Since: base-2.1 | ||||
| Generic All | |||||
Defined in Data.Semigroup.Internal Associated Types
| |||||
| Read All | Since: base-2.1 | ||||
| Show All | Since: base-2.1 | ||||
| Eq All | Since: base-2.1 | ||||
| Ord All | Since: base-2.1 | ||||
| type Rep All | Since: base-4.7.0.0 | ||||
Defined in Data.Semigroup.Internal | |||||
The monoid of endomorphisms under composition.
Endo f <> Endo g == Endo (f . g)
Examples
>>>let computation = Endo ("Hello, " ++) <> Endo (++ "!")>>>appEndo computation "Haskell""Hello, Haskell!"
>>>let computation = Endo (*3) <> Endo (+1)>>>appEndo computation 16
Instances
| Monoid (Endo a) | Since: base-2.1 | ||||
| Semigroup (Endo a) | Since: base-4.9.0.0 | ||||
| Generic (Endo a) | |||||
Defined in Data.Semigroup.Internal Associated Types
| |||||
| type Rep (Endo a) | Since: base-4.7.0.0 | ||||
Defined in Data.Semigroup.Internal | |||||
The dual of a Monoid, obtained by swapping the arguments of (<>).
Dual a <> Dual b == Dual (b <> a)
Examples
>>>Dual "Hello" <> Dual "World"Dual {getDual = "WorldHello"}
>>>Dual (Dual "Hello") <> Dual (Dual "World")Dual {getDual = Dual {getDual = "HelloWorld"}}
Instances
| MonadFix Dual | Since: base-4.8.0.0 | ||||
Defined in Control.Monad.Fix | |||||
| MonadZip Dual | Since: base-4.8.0.0 | ||||
| Foldable Dual | Since: base-4.8.0.0 | ||||
Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldMap' :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # | |||||
| Foldable1 Dual | Since: base-4.18.0.0 | ||||
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Dual m -> m # foldMap1 :: Semigroup m => (a -> m) -> Dual a -> m # foldMap1' :: Semigroup m => (a -> m) -> Dual a -> m # toNonEmpty :: Dual a -> NonEmpty a # maximum :: Ord a => Dual a -> a # minimum :: Ord a => Dual a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Dual a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Dual a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Dual a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Dual a -> b # | |||||
| Traversable Dual | Since: base-4.8.0.0 | ||||
| Applicative Dual | Since: base-4.8.0.0 | ||||
| Functor Dual | Since: base-4.8.0.0 | ||||
| Monad Dual | Since: base-4.8.0.0 | ||||
| Generic1 Dual | |||||
Defined in Data.Semigroup.Internal Associated Types
| |||||
| Data a => Data (Dual a) | Since: base-4.8.0.0 | ||||
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dual a -> c (Dual a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) # toConstr :: Dual a -> Constr # dataTypeOf :: Dual a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) # gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r # gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # | |||||
| Monoid a => Monoid (Dual a) | Since: base-2.1 | ||||
| Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 | ||||
| Bounded a => Bounded (Dual a) | Since: base-2.1 | ||||
| Generic (Dual a) | |||||
Defined in Data.Semigroup.Internal Associated Types
| |||||
| Read a => Read (Dual a) | Since: base-2.1 | ||||
| Show a => Show (Dual a) | Since: base-2.1 | ||||
| Eq a => Eq (Dual a) | Since: base-2.1 | ||||
| Ord a => Ord (Dual a) | Since: base-2.1 | ||||
| type Rep1 Dual | Since: base-4.7.0.0 | ||||
Defined in Data.Semigroup.Internal | |||||
| type Rep (Dual a) | Since: base-4.7.0.0 | ||||
Defined in Data.Semigroup.Internal | |||||
newtype Ap (f :: k -> Type) (a :: k) #
This data type witnesses the lifting of a Monoid into an
Applicative pointwise.
Examples
>>>Ap (Just [1, 2, 3]) <> Ap NothingAp {getAp = Nothing}
>>>Ap [Sum 10, Sum 20] <> Ap [Sum 1, Sum 2]Ap {getAp = [Sum {getSum = 11},Sum {getSum = 12},Sum {getSum = 21},Sum {getSum = 22}]}
Since: base-4.12.0.0
Instances
| Generic1 (Ap f :: k -> Type) | |||||
Defined in Data.Monoid Associated Types
| |||||
| MonadFail f => MonadFail (Ap f) | Since: base-4.12.0.0 | ||||
Defined in Data.Monoid | |||||
| MonadFix f => MonadFix (Ap f) | Since: base-4.12.0.0 | ||||
Defined in Control.Monad.Fix | |||||
| Foldable f => Foldable (Ap f) | Since: base-4.12.0.0 | ||||
Defined in Data.Foldable Methods fold :: Monoid m => Ap f m -> m # foldMap :: Monoid m => (a -> m) -> Ap f a -> m # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m # foldr :: (a -> b -> b) -> b -> Ap f a -> b # foldr' :: (a -> b -> b) -> b -> Ap f a -> b # foldl :: (b -> a -> b) -> b -> Ap f a -> b # foldl' :: (b -> a -> b) -> b -> Ap f a -> b # foldr1 :: (a -> a -> a) -> Ap f a -> a # foldl1 :: (a -> a -> a) -> Ap f a -> a # elem :: Eq a => a -> Ap f a -> Bool # maximum :: Ord a => Ap f a -> a # | |||||
| Foldable1 f => Foldable1 (Ap f) | Since: base-4.18.0.0 | ||||
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Ap f m -> m # foldMap1 :: Semigroup m => (a -> m) -> Ap f a -> m # foldMap1' :: Semigroup m => (a -> m) -> Ap f a -> m # toNonEmpty :: Ap f a -> NonEmpty a # maximum :: Ord a => Ap f a -> a # minimum :: Ord a => Ap f a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Ap f a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Ap f a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Ap f a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Ap f a -> b # | |||||
| Traversable f => Traversable (Ap f) | Since: base-4.12.0.0 | ||||
| Alternative f => Alternative (Ap f) | Since: base-4.12.0.0 | ||||
| Applicative f => Applicative (Ap f) | Since: base-4.12.0.0 | ||||
| Functor f => Functor (Ap f) | Since: base-4.12.0.0 | ||||
| Monad f => Monad (Ap f) | Since: base-4.12.0.0 | ||||
| MonadPlus f => MonadPlus (Ap f) | Since: base-4.12.0.0 | ||||
| (Data (f a), Data a, Typeable f) => Data (Ap f a) | Since: base-4.12.0.0 | ||||
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ap f a -> c (Ap f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ap f a) # toConstr :: Ap f a -> Constr # dataTypeOf :: Ap f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Ap f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Ap f a)) # gmapT :: (forall b. Data b => b -> b) -> Ap f a -> Ap f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r # gmapQ :: (forall d. Data d => d -> u) -> Ap f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Ap f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) # | |||||
| (Applicative f, Monoid a) => Monoid (Ap f a) | Since: base-4.12.0.0 | ||||
| (Applicative f, Semigroup a) => Semigroup (Ap f a) | Since: base-4.12.0.0 | ||||
| (Applicative f, Bounded a) => Bounded (Ap f a) | Since: base-4.12.0.0 | ||||
| Enum (f a) => Enum (Ap f a) | Since: base-4.12.0.0 | ||||
Defined in Data.Monoid | |||||
| Generic (Ap f a) | |||||
Defined in Data.Monoid Associated Types
| |||||
| (Applicative f, Num a) => Num (Ap f a) | Note that even if the underlying Commutativity:
Additive inverse:
Distributivity:
Since: base-4.12.0.0 | ||||
| Read (f a) => Read (Ap f a) | Since: base-4.12.0.0 | ||||
| Show (f a) => Show (Ap f a) | Since: base-4.12.0.0 | ||||
| Eq (f a) => Eq (Ap f a) | Since: base-4.12.0.0 | ||||
| Ord (f a) => Ord (Ap f a) | Since: base-4.12.0.0 | ||||
| type Rep1 (Ap f :: k -> Type) | Since: base-4.12.0.0 | ||||
Defined in Data.Monoid | |||||
| type Rep (Ap f a) | Since: base-4.12.0.0 | ||||
Defined in Data.Monoid | |||||